Page 1
bdkbZ & 2
Áfr’kr % Áfr’kr dk nSfud ,oa O;olkf;d xfrfof/k;ksa esa Á;ksx
lajpuk@foU;kl
2-1 ÁLrkouk
2-2 mn~ns”;
2-3 Áfr”kr
2-3-1 ifjHkk’kk
2-3-2 Áfr”kr dh vo/kkj.k
2-4 Áfr”kr ds vuqÁ;ksx
2-4-1 ykHk ,oa gkfu
2-4-2-deh”ku
2-4-3- NwV ;k fMLdkmaV
2-5- C;kt
2-5-1- lk/kkj.k C;kt
2-5-2- pØo`f) C;kt
2-6- ikB lg;ksxh xfrfof/k;kWa
2-7- lanfHkZr iqLrdsa
2-1 ÁLrkouk %&
lkekU; cksy&pky dh Hkk’kk esa Áfr”kr ls rkRi;Z Áfr lkS(Per Hundred ) mnk- ds fy;s 60 Áfr”kr ls rkRi;Z gqvk 60 Áfr lkS vFkkZr 100 esa ls 60 ;k
60@100 = 6@10 = 3@5
vFkkZr nwljs “kCnksa esa dg ldrs gSa fd Áfr”kr n”keyc ;k fHkUu dks O;Dr
djus dk gh ,d vkSj rjhdk gSA
Page 2
lh/kh vkSj ljy Hkk’kk esa Áfr”kr fdlh la[;k dks 100 ds vuqikr esa O;Dr
djus dk ,d rjhdk gSA vFkkZr~ ge dg ldrs gSa fd tc fdlh fHkUu ds gj
dks 100 cuk nsukA
mnk- 2 2 20
5 5 20
40 40 Áfr”kr
100
blh Ázdkj tc ge dgrs gS fd 30 Áfr”kr ;k 20 Áfr”kr rks bldk vFkZ
gqvk 100 esa ls 30 ;k 100 esa ls 20
Áfr”kr dks n”kkZus ds fy;s % ladsr dk Á;ksx fd;k tkrk gSA Áfr”kr
,d foek ghu jkf”k gS rFkk orZeku le; esa rsth ls bldk Á;ksx c<rk tk
jgk gSA
cSad] O;olk; rFkk cktkj ls lacaf/kr fofHkUu {ks=ksa esa bldk Á;ksx cgqrk;r
ls fd;k tk jgk gSA eq[;r% tc gesa fdlh {ks= dk rqyukRed ;k
fo”ys’k.kRed v/;;u djuk gksrk gS rks ge Áfr”kr dk Á;ksx djuk
ljy gksrk gSaA
mnk- ds fy;s foxr 5 o’kksZa esa ns”k ds eksckby miHksDrkvksa dh la[;k esa
c`f)]
cSadksa esa tek /ku jkf”k esa c`f) ;k deh ] cSadksa esa tek /ku jkf”k ij C;kt
]vk;dj]fcØhdj vkfn lHkh dh x.kuk esa Áfr”kr dk Á;ksx fd;k tkrk gSA
bl v/;k; ds iwoZ dh d{kkvksa esa fo|kFkhZ fHkUu] n”keyo] fHkUu dks
n”keyo esa cnyuk ,oa n”keyo dks fHkUu esa cnyuk lh[k pqds gSaA lkFk
gh lkFk os bu ij vk/kkfjr fofHkUu x.krh; leL;kvksa dks gy djuk tkurs
gSaA
bl v/;k; esa fo|kFkhZ Áfr”kr] fdlh la[;k dks Áfr”kr esa O;Dr
djuk] n”keyc ,oa fHkUu dks Áfr”kr esa O;Dr djuk ;k Áfr”kr dks
n”keyc ,oa fHkUu esa O;Dr djuk rFkk Áfr”kr ij vk/kkfjr vU; x.krh;
o O;ogkfjd leL;kvksa dks gy djuk lh[ksaxsaA
Page 3
2-2 mn~ns”;
bl v/;k; ds v/;;u ds mijkUr Nk= Nk=kvksa esa fuEu O;ogkfjd ifjoZru
gksaxsA
1- fo|kFkhZ fHkUu]n”keyc] vuqikr]Áfr”kr ,oa nj vkfn ds ckjs esa foLr`r
tkudkjh ÁkIr dj ldsxsaA
2- fo|kFkhZ fHkUu] n”keyc] vuqikr] Áfr”kr ,oa nj ds chp varj djus dh
;ksX;rk dk fodkl gksxkA
3- fo|kFkhZ fHkUu] n”keyc] vuqikr dks Áfr”kr esa cnyuk lh[k ldsxsaA
4- fo|kFkhZ fHkUu] n”keyc] vuqikr] Áfr”kr ,oa nj ds chp lca/k LFkkfir
djuk lh[k ldsxsaA
5- fo|kFkhZ fHkUu] n”keyc] vuqikr] Áfr”kr ,oa nj vk/kkfjr leL;kvksa dks
gy djus dh ;ksX;rk dk fodkl gksxkA
6- fo|kFkhZ ykxr ewY;] foØ; ewY; Áfr”kr ykHk] Áfr”kr gkfu tSls ÁR;;ksa
ls ifjfpr gks ldsxsaA
7- fo|kFkhZ ykxr ewY;] foØ; ewY; Áfr”kr ykHk] Áfr”kr gkfu tSls ÁR;;ksa
ls lcaf/kr O;ogkfjd leL;kvksa dks gy djuk lh[k ldsxsA
8- fo|kFkhZ deh”ku] fMLdkmaV tSls ÁR;;ksa ls ifjfpr gks ldsxsaA
9- fo|kFkhZ deh”ku] fMLdkmaV ls lcaf/kr O;ogkfjd leL;kvksa dks gy
djuk lh[k ldsxsaA
10- fo|kFkhZ C;kt]C;kt djus ds Ádkj mi;ksfxrk rFkk C;kt ij vk/kkfjr
O;ogkfjd leL;kvksa dks gy djuk lh[k ldsxsaA
2-3 Áfr”kr %&
tSls fd ge tkurs gSa fd fHkUu n”keyc vkSsj vuqikr ls fo|kFkhZ iwoZ dh
d{kkvksa esa ifjfpr gks pqds gSA vr% Áfr”kr ds f”k{k.k ds iwoZ ;g tku
ysuk vfr vko”;d gS fd fo|kfFkZ;ksa dks fHkUu n”keyc vkSsj vuqikr dk
Hkyh Hkkafr vccks/k gks pqdk gS ;k ughaA bl gsrq f”k{kd dks pkfg, fd og
Page 4
bu ij vk/kkfjr dqN x.krh; leL;kvksa dks fo|kfFkZ;ksa ls gy djok dj
lqfuf”pr dj ys fd fo|kFkhZ Áfr”kr ds f”k{k.k gsrq iw.kZ:Ik ls rS;kj
gSaAlkFk gh lkFk bu leL;kvksa dk d{k esa vH;kLk dj fo|kFkhZ ekufld :Ik
ls Hkh Áfr”kr ds v/;;u ds fy;s rS;kj gks tk;ssxsA bu vH;kLk Á”uksa dh
mi;ksfxrk bl fy;s Hkh gS D;ksafd Áfr”kr fo|kfFkZ;ksa ds fy;s ,dne u;k
ÁR;; gS vkSj ;s vH;kLk Á”u u dsoy fo|kfFkZ;ksa dks iwoZ Kku ls tksMus dk
dk;Z djxs vfirq muesa u;s ÁR;; dks tkuus lh[kus ,oa le>us dh mRlqdrk
Hkh iSnk djsaxsA vr% f”k{kd ds fy;s vko”;d gS fd og tks Hkh Á”u
Nk=ksa dks vH;kl gsrq Ánku djs muesa fHkUurk ]dfBukbZ Lrj dk fo”ks’k
/;ku j[kuk gksxk A
2-3-1 ifjHkk’kk %&
Ekq[; f”k{k.k fcUnq %& fHkUu ]n”keyc]vuqikr] nj ,oa n”eyc ds
ÁR;;ksa
dks le>kuk
f”k{k.k vf/kxe ÁfØ;k %& tSlk fd iwoZ esa gh crk;k tk pqdk gS fd
f”k{k.k vf/kxe ÁfØ;k dh “kq:vkr ,ls Á”uksa ds ek/;e ls dh tkuh
pkfg, tks fd fo|kfFkZ;ksa ds iwoZ Kku ls tqMs gksa rkfd fo|kfFkZ;ksa dks ljyrk
ls iq[; f”k{k.k fcUnq ij yk;k tk lds mnk- ds fy;s 7 ] 9 ] 6 vkfn
fHkUu
15 2 4
dks n”keyc esa ifjoZfrr djus dks dgsa rFkk mlh Ádkj 0-2] 0-03] 0-75]
0-692 vkfn dks fHkUu esa cnyus dks dgsa ijUrq ;gkWa /;ku nsus ;ksX; ckr ;g
gS fd fo|kfFkZ;ksa dks ,lh dksbZ Hkh fHkUu gy djus dks u nsa ftldk gj 0 gks
tSls fd 5 D;ksafd ,sls Á”uksa ls Hkyh Hkkafr ifjfpr u gksus ls fo|kFkhZ
0
HkzfEkr gks ldrs gSaA tc fo|kFkhZ bu Á”uksa dks gy dj ysa rks ekuk tk
ldrk gS fd os vc Áfr”kr lh[kus ds fy;s ekufld :Ik ls rS;kj gSaAvc
gesa lcls igys Áfr”kr dh ifjHkk’kk ls fo|kfFkZ;ksa dks voxr djkuk gksxkA
Page 5
ifjHkk’kk%& Áfr”kr “kCn dh O;qifÙk ysfVu Hkk’kk ds “kCn ijlsaVe ls gqbZ gS
ftldk vFkZ gS Áfr lkS A
Áfr”kr dks O;Dr djus ds fy;s % ladsr dk Á;ksx fd;k tkrk gSA
tSls fd 15%] 20%] 69% vkfnA
bl Ádkj ge dg ldrs gSa fd Áfr”kr fdUgh nks la[;kvksa dk og vuqikr
gS ftldk fd gj 100 gksA
mnk- 1- d{kk 9 ds 79% fo|kfFkZ;ksa ds fgUnh esa vad 60 ls vf/kd vk;sA
vFkkZr ge dg ldrs gSa fd 100 esa ls 79 fo|kFkhZ ,sls gSa ftuds fgUnh esa
vad 60 ls vf/kd gSaA
mnk- 2- ,d fo|ky; esa d{kk 10 ds 20 % fo|kFkhZ vaxzsth fo’k; esa Qsy gks
x;s ;fn fo|ky; esa d{kk 10 esa dqy 500 fo|kFkhZ v/;;ujr gSa rks fdrus
fo|kFkhZ vaxzsth fo’k; esa Qsy gq, \
gy%& mi;qDrZ Á”u esa vaxzsth fo’k; esa Qsy fo|kkfFkZ;ksa dh nj gS 20%
vFkkZr~ Áfr 100 fo|kkfFkZ;ksa esa ls 20 fo|kFkhZ Qsy gq,A
fo|ky; esa d{kk 10 esa dqy 500 fo|kFkhZ v/;;ujr gSa
vFkkZr~ 500 esa ls 20% dh nj ls ge fo|kfFkZ;ksa dh la[;k Kkr dj ysa rks
Qsy fo|kfFkZ;ksa dh la[;k Kkr dh tk Lkdrh gSa
Qsy fo|kfFkZ;ksa dh la[;k nj osl
20 500
100
100
2-3-2 Áfr”kr dh vo/kkj.k
Ekq[; f”k{k.k fcUnq %&
1- Áfr”kr] fHkUu ds :Ik esa
2- Áfr”kr] vuqikr ds :Ik esa
3- Áfr”kr] n”keyc ds :Ik esa
f”k{k.k fof/k %& O;k[;ku fof/k ,oa vH;kl dk leUOk; ds lkFk Á;ksx
lgk;d f”k{k.k lkeXkzh %& Áfr”kr cksMZ] ydMh ;k FkeksZdksy dh
Page 6
vk;rkdkj Vsª] ydMh ds oxkZdkj xqVds ,oa Mk;xzke vkfnA
f”k{k.k vf/kxe ÁfØ;k %&
Áfr”kr dh vo/kkj.k dks Li’V djus ds fy;s vko”;d gS fd fofHkUu :iksa
esa Á;qDr ÁR;;ksa dks Áfr”kr ds lkFk lefUor djds le>k;k tk;sA ;Fkk
1- Áfr”kr] fHkUu ds :Ik esa %&
Eku yhft, fd Nk=ksa dks 8 dks Áfr”kr ds :Ik esa le>kuk gS rks blds
10
fy;s ijEijkxr mikxe dk Á;ksx fd;k tk ldrk gS A ;n~fi ;g fof/k
NksVh d{kkvksa esa vf/kd dkexj gS rFkkfi blds Á;ksx ls Nk=ksa dh vo/kkj.k
dks vklkuh ls Li’V fd;k tk ldrk gSA bl gsrq Áfr”kr cksMZ ydMh ;k
FkeksZdksy dh vk;rkdkj Vsª] ydMh ds oxkZdkj xqVds lgk;d lkexzh ds :I
esa ys ldrs gSaA lgk;d lkexzh dks vkSj vf/kd vkdZ’kd cukus ds fy;s bu
oxkZdkj xqVdksa dks jaxk Hkh tk ldrk gSA
fp= ¼v½ esa ydMh dh vk;rkdkj Vªs ;k FkeksZdksy dk cksMZ fy;k tk
ldrk gS vk;rkdkj Vªs vksj xqVds ysuk FkeksZdksy cksMZ dh rqyuk esa
vf/kd ykHkÁn gS D;ksafd bldk Á;ksx ckj&ckj yacs le; rd fd;k
tk ldrk gS lkFk gh lkFk la[;k cnyus ij dsoy Vsª cnyuh iMsxh
xqVds ogh Á;ksx fd;s tk ldrs gSaA tcfd FkeksZdksy cksMZ dk
j[kj[kkc dfBu gksus ds lkFk&lkFk cukus esa Hkh vf/kd le;
¼v½ ysxsXkk vkSj vyx&vyx la[;kvksa ds fy;s vyx&vyx FkeksZdksy
cksMZ Á;ksx djuk gksxkA ;fn vk;rkdkj Vªs ysa rks fp=kuqlkj
ÁLrqfr gsrq jaxhu oxkZdkj xqVds ysrs gSa vkSj mu xqVdksa dks Vsª esa lsV dj
ysrs gSaA bl Ádkj nl xqVds ckyh Vsª esa 8 xqVds jaxhu lsV djds 8 dh
10
vo/kkj.k dks Li’V fd;k tk ldrk gSSA blh Ádkj vU; dqN fHkUusa TkSls fd
9 ] 14 ] 15 vkfn dks Hkh fp=¼c½¼l½¼n½ }kjk fuEu Ádkj Li’V fd;k tk
10 20 25
Page 7
ldrk gSSA
¼c½ ¼l½ ¼n½
vc bls Áfr”kr :Ik esa O;Dr djus ds fy;s Áfr”kr cksMZ dk Á;ksx djsxsaA
Áfr”kr cksMZ esa 100 oxkZdkj Hkkxksa esa foHkDr gksrk gS 10 Hkkx yackbZ esa rFkk
10 Hkkx PkkSMkbZ esa gksrs gSaA¼fuEukuqlkj½
vc fHkUu 8 dks gh ysa rks Áfr”kr cksMZ esa ÁR;sd 10 Hkkx esa ls 8 Hkkx jaxhu
10
djus gksaxsa rc 100 esa ls 80 Hkkx jaxhu gks tk;saxsa ¼fp= b½
Page 8
bl Ádkj 8 dks Áfr”kr ds :Ik esa 80
10 100
;k 8 1 8 % fy[k ldrs gSaa
100
blh Ádkj 1 dks 1 1 1 % 100 100
25 dks 25 1 25 %
100 100
50 dks 50 1 50 %
100 100
vkfn dks O;Dr fd;k tk ldrk gSA
;s rks ckr gqbZ fHkUu dks Áfr”kr esa cnyus dh vc ;fn Áfr”kr dks fHkUu
esa cnyuk gks rks blh Ádkj O;Dr fd;k tk ldrk gS A
;Fkk
25% 25 1 25 1
100 100 4
50% 50 1 50 1
100 100 2
75% 75 1 75 3
Page 9
100 100 4
80% 80 1 80 4
100 100 5
rFkk
100% 100 1 100 100 1
100 100 100
bl Ádkj Áfr”kr cksMZ ds ek/;e ls fdlh Hkh fHkUu dks Áfr”kr esa ;k
Áfr”kr
dks fHkUu esa cnyuk fo|kfFkZ;ksa dks lqxerk ls fl[kk;k tk ldrk gS A
vH;kl Á”u %&
Kkr dhft,&
1- 800 dk 15@12 Áfr”kr
-----------------------------------------------------
-----------------------------------------------------
2- 100 dk 4@6 Áfr”kr
-----------------------------------------------------
----------------------------------------------------
3- 400 dk 20 Áfr”kr
-----------------------------------------------------
----------------------------------------------------
4- 200 dk ----------------- Áfr”kr 66
---------------------------------------------------
Page 10
---------------------------------------------------
2- Áfr”kr] vuqikr ds :Ik esa %&
Ekku yhft, fd d{kk 9 dh ,d Dykl esa lkekftd foKku fo’k; esa 40 cPpksa
esa ls 35 cPpksa ds 60 ls vf/kd vad vk;s rks fdrus Áfr”kr cPpksa ds 60 ls
vf/kd vad vk;sA
;gkWa 40 esa ls 35 vFkkZr~ 40 cPpksa ds 60 ls vf/kd vad vk;sA vc gesa bls
35
Áfr”kr esa O;Dr djuk gSA vFkkZr~ 100 dks gjkad ds :Ik esa O;Dr djuk
gksxkA vr%
35 100 35 100 1
40 100 40 100
175 1
2 100
87.5 %
mnk- 2- ,d fnu d{kk 9 dh 40 cPpksa dh ,d Dykl esa 20 cPps mifLFkr
jgs rc ml fnu d{kk esa fo|kfFkZ;ksa dh mifLFkfr dk Áfr”kr D;k gSA
gy- 40 fo|kfFkZ;ksa dh d{kk esa mifLFkr fo|kkFkhZ 20
mifLFkfr dk vuqikr 20
40
20 dks 100 ds gjkad ds :Ik esa ifjoZfrZr djuk gksxk
40
Page 11
vr% 20 100
40 100
20 100 1
40 100
50 1
100
50 %
vr% ml fnu d{kk esa 50 % fo|kFkhZ mifLFkfr jgsA
vH;kl Á”u %&
fuEu fHkUuksa dks Áfr”kr esa cnfy;s \
1- 3@4 2- 4@20 3- 15@8 4- 6@40
fuEu Áfr”kr dks fHkUuksa esa cnfy;s \
1- 15% 2- 35% 3- 130% 4- 67%
fjDr LFkkuksa dh iwfrZ dhft,s \
1- 5@6=---- % 2- 5@10=----- % 3- 2@3 =------%
3- Áfr”kr] n”keyc ds :Ik esa %&
Ekku yhft, ;fn d{kk 10 ds ,d fo|kfFkZ us vaxzsth fo’k; esa 50 esa ls
34-5 vad ÁkIr fd;s rks Kkr dhft, fd mls vaxzsth fo’k; esa fdrus
Áfr”kr vad ÁkIr gq, \
;gkWa gesa n”keyc dks igys fHkUu :Ik esa vkSj mlds Ik”pkr~ 100 ds
gjkad esa cnyuk gksxkA
Page 12
gy%& 1- n”keyc dks fHkUu es cnyuk
34-5 345
50 500
2- fHkUu dks 100 ds gjkad eas cnyuk
345 100
500 100
345 100 1
500 100
69 1
100
69 %
blh Ádkj n”keyc dks Áfr”kr :Ik esa O;Dr djuk dqN vU;
mnkgj.ksa ds ek/;e ls Hkh le>k;k tk ldrk gSA tSls fd &
1- 0-65
65
100
65 1
100
65 %
2- 1-33
133
100
133 1
100
133 %
Page 13
2- 0-145
145
1000
145 1
10 100
145 %
10
14-5 %
vH;kl Á”u %&
fuEu n”keyc dks Áfr”kr esa cnfy;s \
1- 0-02 2- 0-05 3 0-374
fuEu Áfr”kr dks esa n”keyc cnfy;s \
1- 75% 2- 35% 3 65%
2-4 Áfr”kr ds vuqÁ;ksx %&
Áfr”kr dk Á;ksx ge gekjs nSfud thou esa cgqrk;r ls djrs gS
Áfr”kr ds vuqÁ;ksxksa dks le>kus ds fy;s f”k{kdksa dks bu nSfud
vko”;drkvksa esa Áfr”kr ds Á;ksx ij fo|kfFkZ;ksa dk /;ku vkdf’kZr
djuk gksxk tSls fd gekjh nSfud thou dh vf/kdka”k vko”;drkvksa dh
iwfrZ gsrq cktkj ls lkeku [kjhnuk iMrk gS rc ÁR;sd lkeku ij
NwV]o`f) vkfn ds fy;s Áfr”kr dk Á;ksx fd;k tkrk gSA cSadks esa iSlk
Page 14
tek djrs le; C;kt dh x.kuk Hkh Áfr”kr esa gh gksrh gSA dkj ,oa ?kj
[kjhnrs le; yksu ysus ij bZ-,e-vkbZ- dh Hkh x.kuk djrs le; Áfr”kr
dk Á;ksx fd;k tkrk gSA
blds vykok vU; {ks=ksa tSls tula[;k]lk{kjrk] mRiknu] e`R;w nj ]tUe
nj ]d`f’k vkfn esa c`f) ;k deh dks O;Dr djus ds fy;s Hkh Áfr”kr dk
gh Á;ksx fd;k tkrk gSA
O;olkf;d xf.kr esa Hkh fofHkUu x.kukvksa gsrq tSls fd ykHk] gkfu] NwV]
deh”ku vkfn dh x.kuk Hkh Áfr”kr dh lgk;rk ls gh dh tkrh gSA
2-4-1 ykHk ,oa gkfu %&
Ekq[; f”k{k.k fcUnq %&
1- ykHk o gkfu dh vo/kkj.kk
2- ykHk o gkfu dh x.kuk djuk
f”k{k.k fof/k %& O;k[;ku fof/k ds lkFk fopkj foe”kZ fof/k dk Á;ksxA
f”k{k.k vf/kxe ÁfØ;k %& fo|kfFkZ;ksa ds fy;s ykHk ]gkfu dh vo/kkj.k
ubZ ugha gSA ykHk ,oa gkfu ls fo|kfFkZ ÁFkfed d{kkvksa esa gh Hkyh Hkafr
Áfjfpr gks pqds gaS rFkk blls lacf)r xf.krh; leL;kvksa dks Hkh gy djuk
lh[k pqds gSaA ek/;fed Lrj ij fo|kfFkZ;ksa dks ykHk gkfu i<kus dk gekjk
eq[; mn~ns”; gS fd mUgsa ykHk gkfu ls lacaf)r O;ogkfjd leL;kvksa ds
lek/kku gsrq rS;kj fd;k tk ldsA
ijUrq tSlk fd ge igys gh dg pqds gS fd f”k{k.k ds iwoZ ;fn f”k{kd
fo|kfFkZ;ksa ds iwoZ Kku ls Hkyh Hkkafr ifjfpr gksxk rks u dsoy f”k{kd dks
vius f”k{k.k dh :ijs[kk cukus esa ljyrk gksxh vfirq fo|kfFkZ Hkh f”k{k.k
dk iwjk&iwjk ykHk ys ldsxsaA
vr% f”k.k dh “kq:vkr igys dqN lkekU; ykHk&gkfu ds Á”uksa ds ek/;e
ls dh tkuh pkfg,A f”k{kd dks pkfg, fd og d{kk esa fo|kfFkZ;ksa ls
Page 15
ykHk&gkfu ds Á”uksa dks gy djokdj ns[k ys fd Nk= ykxr ewY;] foØ;
ewY;] “kq) ykHk] “kq) gkfu] Áfr”kr ykHk] Áfr”kr gkfu tSlh “Cnkcyh ls
Hkyh&Hkkafr ifjfpr gSa fd ugha blls ykHk ;g gksxk fd fo|kfFkZ vkxkeh
f”k{k.k gsrq ekufld :I ls Rs;kj gks tk;sxs rFkk d{k esa Hkh f”k{k.k dk
mÙke okrkoj.k rS;kj gks tk;sxkA
ykxr ewY;%& fdlh Hkh oLrq dks Ø; djrs le; fdlh O;fDr¼xkzgd½}kjk
nh xbZ /ku jkf”k ml oLrq dk ykxr eqY; gksxkA
mnk-%&
jes”k us eksckby dh nqdku ls ,d lselax dk eksckby 11000@& :- esa
[kjhnk rks ;g ewY; jes”k ds fy;s eksckby dk ykxr ewY; ;k Ø; ewY;
gksxkA
eku yhft, jes”k us ;gh eksckby eksgu ¼ fdlh vU; dks½s 11500 : esa csp
fn;k rc eksgu ds fy;s 11500 :- Ø; ewY; gksxk tfodh jes” ds fy;s ;g
foØ; ewY; gksxkA ,slh fLFkfr esa jes”k dks ÁkIr “kq) ykHk D;k gksxk \
gy%& jes”k ds fy;s Ø; ewY; = 11000:-
jes”k ds fy;s foØ; ewY; = 11500:-
“kq) ykHk = jes”k ds fy;s foØ; ewY; & jes”k ds fy;s Ø; ewY;
“kq) ykHk = 11500 :-& 11000:-
“kq) ykHk = 500 :-
bl Ádkj ge dh ldrs gSa fd jes”k us 11000 :- ds ykxr ewY; ij 500
:- dk “kq) ykHk dek;kA
vc ;fn blh ykHk dks Áfr”kr esa O;Dr djuk gks rks bls fuEu Ádkj
djsaxsaA
500 x ;gkWa x Áfr”kr ykHk gSA
11000 100
Page 16
11000 x = 500 100
X = 500 100
11000
x = 50 11
x = 4-54 %
bl Ádkj ge dg ldrs gSa fd jes”k dks eksckby dh fcØh ij 4-54 :-
Áfr 100 :- ds vuqlkj 11000 :- ij dqy 500 :- ykHk ÁIr gqvkA ;gkWa
fo|kfFkZ;ksa dks ;g Hkh Li’V djuk vko”;d gS fd ykhk dh x.kuk lnSo
ykxr ewY; ij dh tkrh gSA
vkb;s ,d vU; mnkgj.k ij fopkj djrsa gSaA
mnk-%& fouksn us ,d ySiVki 18000 :- esa [kjhnk vkSj mls vU; dks
20000 :- esa csp fn;k rc fouksn dks ySiVki cspus ij fdrus Áfr”kr
YkkHk gqvk \
gy%& fouksn ds fy;s ySiVki dk ykxr ewY; ;k Ø; ewY; = 18000 :-
fouksn ds fy;s ySiVki dk ykxr ewY; ;k foØ; ewY; = 20000 :-
“kq) ykHk = foØ; ewY; & Ø; ewY;
“kq) ykHk = 20000 :- & 18000 :-
“kq) ykHk = 2000 :-
vc Áfr”kr ykHk dh x.kuk djrs gSaA
“kq) ykHk 100
Áfr”kr ykHk = Ø; ewY;
2000 100
Áfr”kr ykHk = 18000
100
Áfr”kr ykHk = 9
Page 17
Áfr”kr ykHk = 11-1 %
gkfu %&
tc foØ; ewY;] ykxr ewY; ;k Ø; ewY; ld de gksrk gS rks ,slh fLFkfr
esa gkfu gksrh gS vkSj blds varj dks “kq) gkfu ;k gkfu dgrs gSaA
gkfu = ykxr ewY; ;k Á; ewY; & foØ; ewY;
mnk- %& ?ku”;ke us ,d isVh vkeksa dh 600:- esa [kjhnh rFkk m;s 560 :-
esa cspk crkb, fd ?ku”;ke dks ykHk gqvk ;k gkfu vkSj fdruk \
gy %&
?ku”;ke ds fy;s vkeksa dk Ø; ewYk = 600:-
?ku”;ke ds fy;s vkeksa dk foØ; ewYk = 560:-
Li’V gS fd foØ; ewY;] Ø; ewY; ls de gS vr% ?ku”;ke dks gkfu
gqbZA
gkfu = ykxr ewY; ;k Ø; ewY; & foØ; ewY;
gkfu = 600 :-& 560:-
gkfu = 40 :-
vr% ?ku”;ke dks 40 :- gkfu gqbZA
vc blls Áfr”kr gkfu dh x.kuk djrs gSaA
“kq) gkfu 100
Áfr”kr gkfu = Ø; ewY;
40 100
Áfr”kr gkfu = 600
20
Áfr”kr gkfu = 3
Page 18
Áfr”kr gkfu = 6-6 %
;kn j[ksa %&
1- ykHk @“kq) ykHk = foØ; ewY; & Ø; ewY;
2- gkfu@“kq) gkfu = ykxr ewY; ;k Ø; ewY; & foØ; ewY;
3- ykHk 100
Áfr”kr ykHk = Ø; ewY;
4- gkfu 100
Áfr”kr gkfu = Ø; ewY;
vH;kl Á”u %&
1- ,d O;kikjh us ,d lkbfdy 1200 :- esa [kjhnh ,oa 1500 :-
esa csp nh rks O;kikjh dks ykHk gqvk ;k gkfu vkSj fdrus Áfr”krA
2- nhikyh us ,d jsfM;ks 750 :- es [kjhnk ,oa mls viuh lgsyh
dks 900 :- es csp fn;k rks crkb;s fd nhikyh dks fdrus
Áfr”kr ykHk gqvkA
3- ,d Qy O;kikjh us Qyksa dh 10 Vksdfj;ksa dks 120 :- Áfr
Vksdjh ds fglkc ls [kjhnk ,oa mUgsa 1100 :- esa csp fn;k rks
crkb;s fd O;kikjh dks ykHk gqvk ;k gkfu vkSj fdrus Áfr”kr \
2-4-2-deh”ku %&
Ekq[; f”k{k.k fcUnq %&
1- deh”ku dh vo/kkj.kk
2- deh”ku dh x.kuk djuk
f”k{k.k fof/k %& O;k[;ku fof/k ds lkFk fopkj foe”kZ fof/k dk Á;ksxA
Page 19
f”k{k.k vf/kxe ÁfØ;k %& fo|kFkhZ tkurs gSa fd nSfud thou esa ,sls
cgqr ls {ks= gSa tSls tehu&tk;nkn] chek vkfn dh fcØh djrs le;
Øsrk ,oa fcØsrk ds e/; foØ; lgefr ¼Mhy½ djkus ds fy;s tks rhljk
O;fDr dk;Z djrk gS og u rks Øsrk gksrk gS vksj u gh foØsrk A ;g
rhljk O;fDr Øsrk ,oa foØsrk dks feyckus ls ysdj Mhy Qkbuy gksus
rd e/;LFkrk djrk gS rFkk viuh bl lsok ds cnys mls dqN jkf”k
Ánku dh tkrh gS ftls deh”ku dgrs gSaA ;g deh”ku dh jkf”k Øsrk
,oa foØsrk dh lgefr ij fuHkZj djrh gSA
mnk- chek daifu;ka vius ;gkW ,tsaVksa dh fu;qfDr;ka ftUgsa chek cspus ij
Áfr chek fu/kkZfjr jkf”k Ánku dh tkrh gSA bls deh”ku dgrs gSaA
mnk- 1- %& ,d diMk O;olk;h us vius ;gkW ,d lsYleSu dh fu;qfDr
dh ftls fcØh ij 5% deh”ku fn;k tkrk gSA ;fn mlus 2000 :- ds
diMs dh fcØh dh rks mls fdruk deh”ku feysxk \
gy %& lsYleSu dk deh”ku nj = 5%
fcfØr oLrq dk ewY; = 2000 :-
deh”ku = \
deh”ku = nj fcfØr oLrq dk ewY;
deh”ku = 5% 2000
deh”ku = 5 2000
100
deh”ku = 100 :-
vr% lsYleSu dks 100 :- deh”ku ÁkIr gksxk A
Page 20
mnk-2- %& ,d lsYleSu us ,d tehu dk lkSnk 150000 esa djk;k fFkk
mls ml ij 10 %deh”ku feyrk gS rks crkb;s fd mls fdruk
deh”ku ÁkIr gksxk \
gy %& fcfØr tehu dk ewY; = 150000 :-
deh”ku nj = 10 %
deh”ku = \
deh”ku = nj fcfØr oLrq dk ewY;
deh”ku = 10 % 150000 :-
10 150000 :
deh”ku = 100
deh”ku = 15000 :-
mnk-3- %& ,d O;kikjh us 2500 :- ewY; dk lkeku cspk rFkk mls 150
:- deh”ku ÁkIr gqvk rks crkb;s fd mls fdrus Áfr”kr deh”ku
feyk \
gy %& fcfØr lkeku dk ewY; = 2500 :-
deh”ku nj = \
deh”ku = 150 :-
ekuk fd nj x % gS
deh”ku = nj fcfØr oLrq dk ewY;
150 :- = x % 2500 :-
X 2500 :-
150 :- = 100
Page 21
150 100
X = 2500
X = 6
vr% mls 6 % dh nj ls deh”ku feyk A
vH;kl Á”u %&
1- ,d lsYleSu us 6000 :- dk lkeku cspk rFkk mls 900 :-
deh”ku
ÁkIr gqvk rks deh”kun j Kkr dhft, \
2- ,d lkSns ds Ik”pkr~ ,tsaV dks 15 % nj ls 1350 :- deh”ku
ÁkIr
gqvk rks fcfØr oLrq dk ewY; Kkr dhft, \
3- ,d lsYleSu us dqN lkeku cspk rFkk mls 165 :- deh”ku 3
%ÁkIr gqvk rks fcfØr lkeku dh dher Kkr dhft, \
2-4-3- NwV ;k fMLdkmaV %&
Ekq[; f”k{k.k fcUnq %&
1- NwV ;k fMLdkmaV dh vo/kkj.kk
2- NwV ;k fMLdkmaV dh x.kuk djuk
f”k{k.k fof/k %& O;k[;ku fof/k ds lkFk fopkj foe”kZ fof/k dk Á;ksxA
f”k{k.k vf/kxe ÁfØ;k %& loZÁFke f”k{kd dks pkfg, fd og fofHkUu
mnk-
ds ek/;e ls fo|kfFkZ;ksa ds e/; NwV ;k fMLdkmaV dks Li’V djs tSls fd
Nk=ksa dks fofHkUu mnk- ls Li’V fd;k tk ldrk gS fd cktkj esa cgqr lh
Page 22
,slh oLrq;sa gSa tks fd gesa ml ij vafdr foØ; ewY; ls Hkh de nke ;k
ewY; ij ÁkIr gks tkrh gSaA tSls fofHkUu [kkus dh oLrq;sa] LokLFk; o/kZd is;]
J`axkj dk lkeku vkfnA
vc Á”u mBrk gS fd ,slk dSls gksrk gS \
,slk blfy;s gkdrk gS fd daifu;kWa ;k nqdkunkj mu mRiknksa ij dqN NwV
Ánku djrk gS ftls NwV ;k fMLdkmaV dgrs gSa rFkk ftl nj ls ;g Ánku
dh tkrh gS mls NwV nj ;k fMLdkmaV jsV dgrs gSaA
vr% NwV ;k fMLdkmaV og gS ftldh otg ls dksbZ oLrq ;k lkeku ml ij
vafdr ewY; ls de ewY; ij ÁkIr gksrh gSA
mnkgj.k ds fy;s fofHkUu R;kSgkjksa ;k fo”ks’k voljksa tSls fd nhokyh]
j{kkca/ku] bZn] xkWa/kht;arh] x.kra= fnol ;k Lora=rk fnol vkfn ij feyus
ckyh NwVA
mnk-1- %& eku yhft, fd ,d fÝt dk vafdr ewY; 12000:- gS ijUrq
nhokyh ds volj ij ml ij 15 % NwV nh tk jgh gS tks xzkgd dks fÝt
fdrus :- esa feysxh \
gy%&
fÝt dk vafdr ewY; = 12000:-
fÝt ij nh xbZ NwV dh nj = 15 %
NwV dh jkf”k = \ 12000 15
NwV dh jkf”k = 100
NwV dh jkf”k = 120 15
NwV dh jkf”k = 1800 :-
Ukxn ewY; = vafdr ewY; &NwV
Ukxn ewY; = 12000:- & 1800 :-
Ukxn ewY; = 10200 :-
vr% xzkgd dks fÝt 10200 :- esa feysxh A
Page 23
;gkWa fo|kfFkZ;ksa dks ;g Hkh Li’V djuk vko”;d gS fd ;fn fdlh mRikn
ij ,d lkFk nks Øe”% NwV Ánku dh tk jgh gSa rks bl fLFkfr esa ,d ckj
NwV dh x.kuk djus ds Ik”pkr~ tks uxn ewY; ÁkIr gksxk ml uxn ewY;
ij vxyh NwwV dh x.kuk dh tk;sxhA
mnk- 2-%& 25000 ewY; dh ,d Vh-oh- ij ,d nqdkunkj us nhokyh [kjhnh
ds volj ij 10% ,oa esyk NwV ds rgr 15% fMLdkmaV dk ,syku fd;k
;fn fdlh xzkgd us esys ls nhokyh ds volj ij Vh-oh- [kjhnh rks xzkgd
dks Vh-oh- dk D;k ewY; nsuk gksxk \
gy %&
pwWafd xzkgd us esys ls nhokyh ds volj ij Vh-oh- [kjhnh gS vr% igys
mls esyk NwV dk vkSj mlds Ik”pkr~ nhokyh NwV dk ykHk feysxkA
esyk NwV dh nj = 15%
NwV dh jkf”k = 25000 15
100
NwV dh jkf”k = 3570 :-
Ukxn ewY; = vafdr ewY; &NwV
Ukxn ewY; = 25000:- & 3570 :-
Ukxn ewY; = 21250 :-
Ikqu% nhokyh NwV dh nj = 10%
NwV dh jkf”k = 21250 10
100
Page 24
NwV dh jkf”k = 2125 :-
Ukxn ewY; = 21250:- & 2125 :-
Ukxn ewY; = 19125 :-
vr% esys ls nhokyh ds volj xzkgd dks Vh-oh- [kjhnus ij 19125 :-nsuk
gaksxsA
mnk- 3-%& ,d nqdkunkj 5000 :- dh lkMh ij 35% NwV nsrk gS tfodh
nwljk nqdkunkj mlh lkMh dh [kjhnh ij Øe”k% 10% ,oa 15% dh NwV
nsrk gS rks xzkgd dks fdl nqdkunkj ls lkMh [kjhnuk lgh jgsxk \
gy%&
igys nqdkunkj }kjk nh xbZ NwV dh nj = 35%
NwV dh jkf”k = 5000 35
100
NwV dh jkf”k = 50 35
NwV dh jkf”k = 1750 :-
Ukxn ewY; = vafdr ewY; &NwV
Ukxn ewY; = 5000:- & 1750 :-
Ukxn ewY; = 3250 :-
vc nwljss nqdkunkj }kjk nh xbZ NwV dh nj = 10% ,oa 15%
rc igys 10% NwV dh x.kuk djsaxs ckn esa 15% NwV dh
nwljss nqdkunkj }kjk nh xbZ NwV dh jkf”k = 5000 10
100
Page 25
NwV dh jkf”k = 500 :-
Ukxn ewY; = vafdr ewY; &NwV
Ukxn ewY; = 5000:- & 500 :-
Ukxn ewY; = 4500 :-
iqu% 35% NwV ds fy;s &
NwV dh jkf”k = 4500 15
100
NwV dh jkf”k = 45 15
NwV dh jkf”k = 675 :-
Ukxn ewY; = vafdr ewY; &NwV
Ukxn ewY; = 4500:- & 675 :-
Ukxn ewY; = 3825 :-
vr% igys nqdkunkj ls lkMh [kjhnuk lgh jgsxkA
vH;kl Á”u %&
1- ,d ekbØksoso dk vafdr ewY; 18000 :- gS nadkunkj ml ij
Øe”k% 15% ,oa 10% NwV nsrk gS rks ekbØksoso dk [kjhnh ewY;
D;k gksxk \
2- ,d ?kMh ij vafdr ewY; jkf”k 1500 :- gS A nqdkunkj ml ij
30% NwV nsrk gS rks ?kMh dk Ø; ewY; D;k gksxk \
3- ,d vyekjh dh dher 5000 : gS nadkunkj ml ij 1000:- dh
NwV nsrk gS rks nqdkunkj us ml ij fdrus Áfr”kr dh NwV nh \
Page 26
2-5- C;kt%&
Ekq[; f”k{k.k fcUnq %&
1- lk/kkj.k C;kt dh vo/kkj.kk
2- ljy C;kt dh x.kuk djuk
3- pØo`f) C;kt dh vo/kkj.kk
4- pØo`f) C;kt dh x.kuk djuk
f”k{k.k fof/k %& O;k[;ku fof/k ds lkFk fopkj foe”kZ fof/k ,oa lw= gsrq
fuxeu fof/k dk Á;ksx,oa vH;kl dk;ZA
f”k{k.k vf/kxe ÁfØ;k %&vHkh rd ds f”k{k.k mijkar ge ;g tkurs gSa
fd Nk=&Nk=k;s nj] Áfr”kr] Ø; ewY;] foØ; ewY;] ykHk&gkfu NwV vkfn
fofHkUu xf.krh; leL;kvksa rFkk muds gy ls Hkyh&Hkkafr ifjfpr gks pqds gSaA
vc le; gS fd fo|kfFkZ;ksa dks C;kt ls ifjfpr djk;k tk;sA
d{kk esa fdlh Nk= ds lEeq[k ,d dkYifud ifjfLFkfr j[kdj iwWaNk tk
ldrk gS fd ;fn mls fdlh oLrq dks [kjhnuk gks vkSj mlds ikl mruh
jkf”k ugha gks rks og D;k djsxkA fu”pr :I ls Nk= dk tckc gksxk fd
og fdlh ls mruh jkf”k m/kkj ys ysxk vkSj ml oLrq ;k lkeku dks [kjhn
ysxkA vc mls ;g le>kuk pkfg, fd ;fn m/kkj nsus ckyk O;fDr mldk
ifjfpr ;k fe= ugha gS rks og D;ksa fdlh Hkh O;fDr dks ,sls gh m/kkj nsxkA
,sls esa Nk= tckc nsxk fd ;fn og dqN vfrfjDr jkf”k ml O;fDr dks
nsxk rks og O;fDr mls m/kkj ns nsxkA
bl mnkgj.k ds Ik”pkr~ fo|kfFkZ;ksa dks le>k;k tk ldrk gS fd tc fdlh
vko”;drk ds dkj.k tc ge fdlh vU; O;fDr ls dqN jkf”k fuf”pr
le; ds fy;s m/kkj ysrs gSa vkSj mls fu/kkfjZr le; ds Ik”pkr~ vfrfjDr
jkf” ds lkFk okil dj nsrs gSa rks nh xbZ vfrfjDr jkf”k C;kt dgykrh
gSA
mnkgj.k ds fy;s eku yhft, fd lksgu us vius fe= ls 500 :- ,d o’kZ
ds fy;s m/kkj fy;s vkSj ,d o’kZ Ik”pkr~ 550 :- okil fd;s rks lksgu }kjk
vius fe= dks fn;s x;s vfrfjDr 50 :- C;kt dgyk;sxkA
;gkW fo|kfFkZ;ksa dks ;g Hkh Li’V djuk mfpr gksxk fd m/kkj nh xbZ jkf”k
Page 27
ewy/ku rFkk C;kt lfgr okil fd;k x;h jkf”k vFkkZr C;kt lfgr ewy/ku
feJ/ku dgykrk gSA
fdlh ewy/ku ij fdruk C;kt yxsxk ;g _.knkrk ¼nsunkj½ rFkk
_.kxzkgrk¼dtZnkj½ ds chp iwoZ fu/kkZfjr “krkZsa ij fuHkZj djrk gS a
tSls f dewy jde ;k ewy/ku fdruk gS] fdrus le; esa ckil fd;k
tk;sxkvkSj fdl nj ls vFkkZr~ Áfr 100 :- ij fdruh vfrfjDr
/kujkf”k nsuh gksxhA
C;kt dh x.kuk nks Ádkj ls dh tkrh gSA
1- lk/kkj.k C;kt
2- pØo`f) C;kt
2-5-1- lk/kkj.k C;kt %&
f”k{k.k vf/kxe ÁfØ;k %& tSlk fd ge tkurs gSa fd fdlh fuf”pr /ku
jkf”k ij fuf”pr le; mijkar fuf”pr nj ls ns; jkf”k dks C;kt dgts
gSaA
mnk- 1-%& eku yhft;s fd vafdr us vius fe= t;s”k ls dkj [kjhnus ds
fy;s 3 o’kZ ds fy;s 10% nj ls 200000 :- m/kkj fy;s rks 3 o’kZ ckn
vafdr t;s”k dks fdruh /kujkf”k okil djsxk \
mDr mnkgj.k esa vafdr us t;s”k ls dkj [kjhnus 200000 :- m/kkj fy;s
vFkkZr~ ewy/ku = 200000 :- ] nj = 10%
vc ns[krs gSa fd ,d o’kZ ckn vafdr dks fdruk /kujkf”k okil djuk
gksxh
200000 10
,d o’kZ ckn ns; jkf”k = 100 --------------------------¼1½
vr% ,d o’kZ ckn ns; jkf”k = 20000:-
bl Ádkj rhu o’kZ ckn = 3 20000 ------------------------------¼2½
Page 28
bl Ádkj rhu o’kZ ckn = 60000 :-
vFkkZr~ vafdr dks rhu o’kZ ckn t;s”k dks 60000 :- vfrfjDr nsuk gksxk
vFkkZr~ dqy
200000 :-¼ewy/ku½-$ 60000 :-¼C;kt½ = 200000 :-¼feJ/ku½ okil
djus gksaxsA
;gkWa ,d ckr xkSj djus dh gS fd rhuksa o’kksZa ds fy;s ,d gh ewy/ku
¼200000 :-½ fy;k x;k gSA bl Ádkj ls tc C;kt dh x.kuk dh tkrh gS
rks bls lk/kkj.k C;kt dgrs gaSA
vFkkZr~ ge dg ldrs gSa fd tc C;kt dh x.kuk esa ewy/ku jkf”k esa dksbZ
ifjoZru ugha gksrk rc bls lk/kkj.k C;kt dgrs gaSA
mi;qDrZ mnkgj.k esa ;fn ge in ¼1½ rFkk in ¼2½ ij xkSj djsa rks ge
ns[krsa gSa fd nksuks inksa dks feykdj ,d gh ckj esa lk/kkj.k C;kt dh x.kuk
dh tk ldrh gS
200000 10 3
lk/kkj.k C;kt = 100
lk/kkj.k C;kt = 60000 :- lw= %&
ewy/ku nj le;
lk/kkj.k C;kt = 100
mnk- 2-%& foØkar us ,d IykV [kjhnus ds fy;s _.knkrk daiuh ls
500000 :- 2 o’kZ ds fy;s 15% lk/kj.k C;kt ij m/kkj fy;s rks 2 o’kZ
ckn foØkar dks _.knkrk daiuh dks fdruh /ku jkf”k okil djuh gksxh \
gy%&
;gkWa ewy/ku = 500000 :-
nj = 15%
le; = 2 o’kZ
Page 29
ewy/ku nj le;
lk/kkj.k C;kt = 100 500000 15 2
lk/kkj.k C;kt = 100
lk/kkj.k C;kt = 5000 15 2
lk/kkj.k C;kt = 150000
vr% rhu o’kZ dk C;kt 150000 :- gksxk A
rhu o’kZ ckn foØkar }kjk _.knkrk daiuh dks okil dh tkus okyh
/ku jkf”k = ewy/ku $C;kt
= 500000 $150000
= 650000 :-
mnk- 3-%& ,d O;fDr us ,d Qkbusal daiuh ls 50000 :- 6% C;kt ls 6
ekg ds fy;s m/kkj fy;s rks 6 ekg Ik”pkr~ fdruh /ku jkf”k Qkbusal daiuh
dks okil djuh gksxh \
gy %& ;gkWa ewy/ku = 50000 :-
nj = 6 %
le; = 6 ekg = 1@2 o’kZ
ewy/ku nj le;
lk/kkj.k C;kt = 100
50000 6 1
Page 30
lk/kkj.k C;kt = 100 2
lk/kkj.k C;kt = 1500
vr% 6 ekg ckn ns; /ku jkf”k = ewy/ku $C;kt
= 50000 $1500
= 51500 :-
Lkk/kkj.k C;kt dh x.kuk esa tks ckr /;ku nsus ;ksX; gS og ;g gS fd dbZ
ckj le; dh x.kuk ekg esa dj yh tkrh gS tSls fd =Sekfld] N%ekgh]
;k vkB ekg vkfn ,slh fLFkfr esa ekg dks lnSo o’kZ esa ifjofrZr dj ysuk
pkfg, vkSj ;fn bl Ádkj ds mnkgj.kksa dks fo|kfFkZ;ksa ds lEeq[k j{kdj
mudk vH;kl djk fn;k tk;s rks fo|kfFkZ;ksa ds fy;s lk/kkj.k C;kt dh
x.kuk vkSj vf/kd Li’V o ljy gks tk;sxhA
vH;kl Á”u %&
fuEu ls lk/kkj.k C;kt dh x.kuk dhft, \
1- ewy/ku = 2000 :- nj = 3 % le; = 4 ekg
2- ewy/ku = 5000 :- nj = 5 % le; = 6 ekg
3- ewy/ku = 20000 :- nj = 10 % le; = 12 ekg
4- oS”kkyh us viuh Mªsl [kjhnus ds fy;s e/kqfjek ls 1500 :-
m/kkj fy;s 3 ekg Ik”pkr~ 3 % nj ls mls fdruh /kujkf”k
e/kqfjek dks nsuh gksxh \
2-5-2- pØo`f) C;kt %&
Page 31
f”k{k.k vf/kxe ÁfØ;k %& ge igys gh fo|kkfFkZ;ksa dks crk pqds gSa fd
l/kkj.k C;kt dh x.kuk esa le; fdruk Hkh gks eqy/ku leku gh jgrk gS
rFkk mlh ewy/ku ij fu/kkZfjr nj ls C;kt dh x.kuk dh tkrh gSA ijUrq
dbZ ckj ns[kk tkrk gS fd x.kuk djrs le; C;kt ij Hkh C;kt yxk;k
tkrk gSA bls fuEu mnkgj.k ds ek/;e ls le>rs gSaA
mnk-1- %& ekuk fd fo|k us 1000 :- 2 o’kZ ds fy;s 4 % okf’kZd nj ls
ehjk dks bl “krZ ds lkFk fn;s fdmls C;kt ij Hkh C;kt nsuk gksxk rks Kkr
dhft, fd ehjk dks fdruh /kujkf”k fo|k dks okil djuh gksxh \
gy %& pwWafd ;gkWa C;kt ij Hkh C;kt dh x.kuk djuh gS vr% igys ,d
o’kZ dk C;kt Kkr djsaxsa vkSj ml C;kt dks ewy/ku esa tksM dj iqu% ewy/ku
Kkr dj fQjls C;kt dh x.kuk djsaxsA
ÁFke o’kZ ds fy;s ewy/ku = 1000 :- nj = 4 % le; = 1 o’kZ
ewy/ku nj le;
lk/kkj.k C;kt = 100
1000 4 1
lk/kkj.k C;kt = 100
lk/kkj.k C;kt = 40:-
nwljs o’kZ ds fy;s ewy/ku = ewy/ku $ C;kt
ewy/ku = 1000 $ 40
ewy/ku = 1040 :-
ewy/ku nj le;
nwljs o’kZ dk lk/kkj.k C;kt = 100
Page 32
1040 4 1
nwljs o’kZ dk lk/kkj.k C;kt = 100
nwljs o’kZ dk lk/kkj.k C;kt = 41-6 :-
bl Ádkj nwljs o’kZ Ik”pkr~ okil dh tkus okyh /kujkf”k = 1040 $41-6
= 1081-6 :-
vr% 2 o’kZ ckn ehjk fo|k dks 1081-6 :-okil djsxhA
mi;qDrZ mnkgj.k ij xkSj djsa rks ik;sxs fd ;gkWa C;kt dh x.kuk esa nj rks
leku gS ijUrq ewy/ku Áfro’kZ cny jgk gS A
tc C;kt dh x.kuk esa nj rks leku jgs ijUrq ewy/ku Áfro’kZ cny
tk;s rks bl Ádkj ds C;kt dks pØo`f) C;kt dgrsa gSaA
mnk-2- %& ,d O;fDr us 500 :- 5 % pØo`f) C;kt dh nj ls 4 o’kZ ds
fy;s m/kkj fy;s rks 4o’kZ ckn mls _.knkrk dks fdruh jkf”k okil djuh
gksxh \
ÁFke o’kZ ds fy;s ewy/ku = 500 :- nj = 5 % le; = 1 o’kZ
ewy/ku nj le;
lk/kkj.k C;kt = 100
500 5 1
lk/kkj.k C;kt = 100
lk/kkj.k C;kt = 25 :-
nwljs o’kZ ds fy;s ewy/ku = ewy/ku $ C;kt
Page 33
ewy/ku = 500 $ 25
ewy/ku = 525 :-
525 5 1
nwljs o’kZ dk lk/kkj.k C;kt = 100
nwljs o’kZ dk lk/kkj.k C;kt = 26-25 :-
bl Ádkj rhljs o’kZ ds fy;s ewy/ku = 525 $26-25
= 551-25 :-
Rkhljs o’kZ dk C;kt
551-25 5 1
lk/kkj.k C;kt = 100
lk/kkj.k C;kt = 27-56 :-
vc Rkhljs o’kZ vkn vFkkZr~ pkSFks o’kZ dk ewy/ku = ewy/ku $ C;kt
ewy/ku = 551-25 $ 27-56
ewy/ku = 578-81 :-
578-81 5 1
pkSFks o’kZ dk lk/kkj.k C;kt = 100
nwljs o’kZ dk lk/kkj.k C;kt = 28-94 :-
vr% pkSFks o’kZ ckn ewy/ku = ewy/ku $ C;kt
ewy/ku = 578-81$ 28-94
ewy/ku = 607-75 :- okil djusa gksaxsA
Page 34
pØo`f) C;kt dk lw= %&
ekuk fd ewy/ku P nj r rFkk le; t gks rks
ewy/ku nj le;
ÁFke o’kZ dk C;kt = 100
P r 1
ÁFke o’kZ dk C;kt = 100
P r
= 100
,d o’kZ ckn nwljs o’kZ ds fy;s ewy/ku = ewy/ku $ C;kt
ewy/ku = P $ P r 100
ewy/ku = P(1+ r / 100 )
P(1+ r / 100 ) r 1 nwljs o’kZ dk lk/kkj.k C;kt = 100
nwljs o’kZ dk lk/kkj.k C;kt = P(1+ r / 100 )(r/100) bl Ádkj rhljs o’kZ ds fy;s
ewy/ku = P(1+ r / 100 )+ P(1+ r / 100 )(r/100)
ewy/ku = P(1+ r / 100 )[1+ (r/100)]
ewy/ku = P(1+ r / 100 )(1+ r/100)
ewy/ku = P(1+ r / 100 )² ..........................( A)
Page 35
P(1+ r / 100 )² r 1
rhljs o’kZ dk C;kt = 100
rhljs o’kZ dk C;kt = P(1+ r / 100 )² (r/100)
rhljs o’kZ ckn ns; jkf”k = ewy/ku $ C;kt
= P(1+ r / 100 )² + P(1+ r / 100 )² (r/100)
= P(1+ r / 100 )² (1+ r/100)
= P(1+ r / 100 )³............................ ( B)
bl Ádkj leh- (A) vkSj( B) ls Li’V gS fd ;fn ge t o’kZ ckn ns; jkf”k
Kkr djsa rks
t o’kZ ckn ns; dqy jkf”k = P(1+ r / 100 )t ......................... (C)
ijUrq ge tkurs gSaA fd ÁkjafHkd ewy/ku P gSA
rc t o’kZ ckn C;kt dh jkf”k = P(1+ r / 100 )t - P
= P[(1+ r / 100 )t - 1].................. ( D)
mi;qDrZ leh- (C) t o’kZ ckn ns; dqy jkf”k vkSj( D) t o’kZ ckn C;kt dh
jkf”k dh x.kuk lh/ks leh- esa ewy/ku] nj] o le; ds ekuksa dks j[kdj Kkr
dh tk ldrh gSA
pØo`f) C;kt = ewy/ku[(1+nj@100½le;
-1]
feJ/ku = ewy/ku$C;kt
mnk-3- %& ,d O;fDr us 1200 :- 3 o’kZ ds fy;s 5 % okf’kZd pØo`f)
C;kt dh nj ls m/kkj fy;s rks mls rhu o’kZ ckn fdruk C;kt nsuk gksxk \
gy %&
ge tkurs gSa fd t o’kZ ckn C;kt dh jkf”k = P[(1+ r / 100 )t - 1]
Page 36
;gkWa P = 1200 r = 5 % t = 3 o’kZ
3 o’kZ ckn C;kt dh jkf”k = 1200[(1+ 5/ 100 )3 - 1]
= 1200 [(105/ 100 )3 - 1]
= 1200[(105/ 100) (105/ 100) (105/ 100) - 1]
= 1200 [1157625/1000000- 1]
= 1200 [1157625-1000000/1000000]
= 1200 [157625/1000000]
= 1200 [0.157625]
= 189.15
vr% rhu o’kZ ckn mls 189.15:-C;kt nsuk gksxkA
;kn j[ksa %&
ewy/ku nj le;
lk/kkj.k C;kt = 100
pØo`f) C;kt = ewy/ku[(1+nj@100½le;
-1]
feJ/ku = ewy/ku$C;kt
Page 37
vH;kl Á”u %&
fuEu ls pØo`f) C;kt dh x.kuk dhft, \
1- ewy/ku = 2000 :- nj = 3 % le; = 4 o’kZ
2- ewy/ku = 5000 :- nj = 5 % le; = 6 o’kZ
3- ewy/ku = 20000 :- nj = 10 % le; = 2o’kZ
4 dksbZ ewy/ku fdrus le; Ik”pkr~ 8 Áfr”kr nj ls nqxuk gks tk;sxk
\
2-6- ikB lg;ksxh xfrfof/k;kWa %&
1- fo|kfFkZ;ksa dks ,d ekg dh mudh d{kk dh mifLFkfr jftLVj dh Áfr
miyC/k djkdj muls d{kk ds Nk= ,oa Nk=kvksa dh mifLFkfr dk Áfr”kr
Kkr djus dks dgsaA
2- fo|kfFkZ;ksa dks dgsa fd os vius ekrk&firk ds lkFk cktkj tk;sa vkSj [kjfns
x;s lkeku dh fyLV cuk;sa ftlesa mu ij vafdr ewY;] uxn ewY; o NwV
dk mYys[k gksA
3- pkVZ iwjk dj ykus dks dgsaA
l-Ø- vafdr ewY; foØ; ewY; ykHk gkfu Áfr”kr
1- 700:- 650:- ------- ------------- -----------
2- 480:- ----- 25 ---------- ---------
3- 500:- ------- ------------- 40 ----------
4- 1000:- -------- -------------- 100 ---------------
2-7- lanfHkZr iqLrdsa %&
1- Mangal S.K. : Teaching of Mathematics, Arya Book Depot,
New Delhi.
Page 38
2. Siddhu, K. S. : Teaching of Mathematics,Sterling Publishers,
New Delhi.
3. C.Papola (2006): Teaching of Mathematics, Anmol Publications
Pvt., New Delhi.
4. Sudhir Kumar & D.N. Ratnalikar: Teaching of Mathematics,
Anmo Publications Pvt., New Delhi.
5. Prof.Ram sharan & Manju Sharma: Teaching of Mathematics,
A.P.H.Publishing Corporation,5 Ansari Road,Darya Ganj, New Delhi.
6. MkWa- lksju flag % xf.kr f”k{k.k ] lkfgR; Ádk”ku ]vkxjk m-Á-
7. ,e-,l-jkor ,oa ,e-ch-yky vxzoky ] fouksn iqLrd eafnj vkxjk m-Á-